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Selected Topics in Cosmic Ray Physics

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Multiple Messengers and Challenges in Astroparticle Physics

Abstract

The search for the origin of cosmic rays is as active as ever, mainly driven by new insights provided by recent pieces of observation. Much effort is being channelled in putting the so-called supernova paradigm for the origin of galactic cosmic rays on firmer grounds, while at the highest energies we are trying to understand the observed cosmic-ray spectra and mass composition and relating them to potential sources of extragalactic cosmic rays. Interestingly, a topic that has acquired a dignity of its own is the investigation of the transition region between the galactic and extragalactic components, once associated with the ankle and now increasingly thought to be taking place at somewhat lower energies. Here, we summarize recent developments in the observation and understanding of galactic and extragalactic cosmic rays and we discuss the implications of such findings for the modelling of the transition between the two.

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Notes

  1. 1.

    Here we do not consider the case of neutrons because their decay time is much shorter than all other scales involved in the propagation of UHECR [241, 242].

  2. 2.

    Also referred as GZK cutoff or suppression.

  3. 3.

    We will not discuss here the case of the possible presence of extragalactic magnetic fields, we will come back to this point in the forthcoming section “Intergalactic Magnetic Fields”.

  4. 4.

    Given a distribution of sources with a number density \(n_S\) each with the same luminosity \(L_S\), the energy emitted per unit time and volume (emissivity) is given by \(\mathcal{L}_S=n_SL_S\).

  5. 5.

    For a recent detailed discussion of EMC development on CMB and EBL see [299] and references therein.

  6. 6.

    Distance at which the peripheral velocity of the star reaches the speed of light \(2\pi R_L/P=c\) and the magnetic field lines spiral outwards along the azimuth.

References

  1. W.D. Apel et al., Astropart. Phys. 31, 86 (2009). https://doi.org/10.1016/j.astropartphys.2008.11.008

  2. B. Bartoli et al., Phys. Rev. D 92(9), 092005 (2015). https://doi.org/10.1103/PhysRevD.92.092005

  3. A.R. Bell, Mon. Not. R. Astron. Soc. 182, 147 (1978)

    Article  ADS  Google Scholar 

  4. V. Ptuskin, J. Phys. Conf. Ser. 47, 113 (2006). https://doi.org/10.1088/1742-6596/47/1/014

  5. P. Blasi, E. Amato, JCAP 1201, 011 (2012). https://doi.org/10.1088/1475-7516/2012/01/011

  6. O. Adriani et al., Astrophys. J. 791(2), 93 (2014). https://doi.org/10.1088/0004-637X/791/2/93

  7. M. Aguilar, L. Ali Cavasonza, G. Ambrosi, L. Arruda, N. Attig, S. Aupetit, P. Azzarello, A. Bachlechner, F. Barao, A. Barrau et al., Phys. Rev. Lett. 117(23), 231102 (2016). https://doi.org/10.1103/PhysRevLett.117.231102

  8. J. Vink, Astron. Astrophys. Rev. 20, 1 (2012). https://doi.org/10.1007/s00159-011-0049-1

  9. V.N. Zirakashvili, V.S. Ptuskin, H.J. Volk, Astrophys. J. 678, 255 (2008). https://doi.org/10.1086/529579

  10. H.J. Volk, E.G. Berezhko, L.T. Ksenofontov, Astron. Astrophys. 433, 229 (2005). https://doi.org/10.1051/0004-6361:20042015

  11. A. Bell, K. Schure, B. Reville, G. Giacinti, Mon. Not. R. Astron. Soc. 431, 415 (2013). https://doi.org/10.1093/mnras/stt179

  12. M. Cardillo, E. Amato, P. Blasi, Astropart. Phys. 69, 1 (2015). https://doi.org/10.1016/j.astropartphys.2015.03.002

  13. A.W. Strong, I.V. Moskalenko, Ap. J. 509, 212 (1998). https://doi.org/10.1086/306470

  14. C. Evoli, D. Gaggero, D. Grasso, L. Maccione, JCAP 10, 018 (2008). https://doi.org/10.1088/1475-7516/2008/10/018

  15. R. Kissmann, Astropart. Phys. 55, 37 (2014). https://doi.org/10.1016/j.astropartphys.2014.02.002

  16. D. Maurin, F. Donato, R. Taillet, P. Salati, Ap. J. 555, 585 (2001). https://doi.org/10.1086/321496

  17. O. Adriani et al., Science 332, 69 (2011). https://doi.org/10.1126/science.1199172

  18. M. Aguilar et al., Phys. Rev. Lett. 114, 171103 (2015). https://doi.org/10.1103/PhysRevLett.114.171103

  19. M. Aguilar et al., Phys. Rev. Lett. 115(21), 211101 (2015). https://doi.org/10.1103/PhysRevLett. 115.211101

  20. S. Thoudam, J.R. Hrandel, Mon. Not. R. Astron. Soc. 435, 2532 (2013). https://doi.org/10.1093/mnras/stt1464

  21. S. Thoudam, J.R. Hrandel, Astron. Astrophys. 567, A33 (2014). https://doi.org/10.1051/0004-6361/201322996

  22. N. Tomassetti, Astrophys. J. 752, L13 (2012). https://doi.org/10.1088/2041-8205/752/1/L13

  23. P. Blasi, E. Amato, P.D. Serpico, Phys. Rev. Lett. 109, 061101 (2012). https://doi.org/10.1103/PhysRevLett.109.061101

  24. R. Aloisio, P. Blasi, JCAP 1307, 001 (2013). https://doi.org/10.1088/1475-7516/2013/07/001

  25. O. Adriani et al., Nature 458, 607 (2009). https://doi.org/10.1038/nature07942

  26. M. Aguilar et al., Phys. Rev. Lett. 110, 141102 (2013). https://doi.org/10.1103/PhysRevLett.110.141102

  27. O. Adriani et al., Phys. Rev. Lett. 102, 051101 (2009). https://doi.org/10.1103/PhysRevLett.102.051101

  28. P.D. Serpico, Astropart. Phys. 39–40, 2 (2012). https://doi.org/10.1016/j.astropartphys.2011.08.007

  29. O. Adriani et al., Phys. Rev. Lett. 111, 081102 (2013). https://doi.org/10.1103/PhysRevLett.111.081102

  30. M. Aguilar et al., Phys. Rev. Lett. 113, 121102 (2014). https://doi.org/10.1103/PhysRevLett.113.121102

  31. P. Blasi, Phys. Rev. Lett. 103, 051104 (2009). https://doi.org/10.1103/PhysRevLett.103.051104

  32. P. Blasi, P.D. Serpico, Phys. Rev. Lett. 103, 081103 (2009). https://doi.org/10.1103/PhysRevLett.103.081103

  33. D. Hooper, P. Blasi, P.D. Serpico, JCAP 0901, 025 (2009). https://doi.org/10.1088/1475-7516/2009/01/025

  34. S. Profumo, Cent. Eur. J. Phys. 10, 1 (2012). https://doi.org/10.2478/s11534-011-0099-z

  35. M. Aguilar, L. Ali Cavasonza, B. Alpat, G. Ambrosi, L. Arruda, N. Attig, S. Aupetit, P. Azzarello, A. Bachlechner, F. Barao et al., Phys. Rev. Lett. 117(9), 091103 (2016). https://doi.org/10.1103/PhysRevLett.117.091103

  36. P. Lipari, Phys. Rev. D 95(6), 063009 (2017). https://doi.org/10.1103/PhysRevD.95.063009

  37. B. Katz, K. Blum, J. Morag, E. Waxman, MNRAS 405, 1458 (2010). https://doi.org/10.1111/j.1365-2966.2010.16568.x

  38. K. Blum, B. Katz, E. Waxman, Phys. Rev. Lett. 111(21), 211101 (2013). https://doi.org/10.1103/PhysRevLett.111.211101

  39. A. Aab et al., Phys. Rev. D 90(12), 122005 (2014). https://doi.org/10.1103/PhysRevD.90.122005

  40. D. Allard, Astropart. Phys. 39–40, 33 (2012). https://doi.org/10.1016/j.astropartphys.2011.10.011

  41. K. Fang, K. Kotera, A.V. Olinto, Astrophys. J. 750, 118 (2012).https://doi.org/10.1088/0004-637X/750/2/118

  42. R. Aloisio, V. Berezinsky, P. Blasi, JCAP 1410(10), 020 (2014).https://doi.org/10.1088/1475-7516/2014/10/020

  43. R.U. Abbasi et al., Astropart. Phys. 64, 49 (2015). https://doi.org/10.1016/j.astropartphys.2014.11.004

  44. T. Kobayashi, Y. Komori, K. Yoshida, J. Nishimura, Astrophys. J. 601, 340 (2004). https://doi.org/10.1086/380431

  45. M. Ackermann et al., Phys. Rev. Lett. 108, 081104 (2012). https://doi.org/10.1103/PhysRevLett.108.011103

  46. C.R. Data Base (2017), http://lpsc.in2p3.fr/crdb

  47. S. Abdollahi et al., Phys. Rev. Lett. 118(9), 091103 (2017). https://doi.org/10.1103/PhysRevLett.118.091103

  48. F. Aharonian et al., Astron. Astrophys. 508, 561 (2009). https://doi.org/10.1051/0004-6361/200913323

  49. D. Staszak, in PoS ICRC2015, vol. 411 (2016)

    Google Scholar 

  50. S. Abdollahi et al., Phys. Rev. D 95(8), 082007 (2017). https://doi.org/10.1103/PhysRevD.95.082007

  51. I. De Mitri et al., EPJ Web Conf. 136, 02010 (2017). https://doi.org/10.1051/epjconf/201713602010

  52. P.S. Marrocchesi, Nucl. Instrum. Meth. A692, 240 (2012). https://doi.org/10.1016/j.nima.2011.12.108

  53. Y. Asaoka et al., Astropart. Phys. 91, 1 (2017). https://doi.org/10.1016/j.astropartphys.2017.03.002

  54. M. Aguilar et al., Phys. Rev. Lett. 113, 221102 (2014). https://doi.org/10.1103/PhysRevLett.113.221102

  55. K. Sakai, et al., in PoS ICRC2015, vol. 436 (2016)

    Google Scholar 

  56. T. Aramaki, C.J. Hailey, S.E. Boggs, P. von Doetinchem, H. Fuke, S.I. Mognet, R.A. Ong, K. Perez, J. Zweerink, Astropart. Phys. 74, 6 (2016). https://doi.org/10.1016/j.astropartphys.2015.09.001

  57. H.S. Ahn et al., Astrophys. J. 714, L89 (2010). https://doi.org/10.1088/2041-8205/714/1/L89

  58. Y.S. Yoon et al., Astrophys. J. 839(1), 5 (2017). https://doi.org/10.3847/1538-4357/aa68e4

  59. E. Atkin et al., Astropart. Phys. 90, 69 (2017). https://doi.org/10.1016/j.astropartphys.2017.02.006

  60. E.S. Seo, Astropart. Phys. 39–40, 76 (2012). https://doi.org/10.1016/j.astropartphys.2012.04.002

  61. N. Picot-Clemente, et al., in PoS ICRC2015, vol. 425 (2015)

    Google Scholar 

  62. A. Oliva, et al., in PoS ICRC2015, vol. 425 (2015)

    Google Scholar 

  63. G. Kulikov, G. Khristiansen, J. Exp. Theor. Phys. 35, 635 (1958)

    Google Scholar 

  64. J. Blumer, R. Engel, J.R. Horandel, Prog. Part. Nucl. Phys. 63, 293 (2009). https://doi.org/10.1016/j.ppnp.2009.05.002

  65. J.R. Hoerandel, Astropart. Phys. 21, 241 (2004). https://doi.org/10.1016/j.astropartphys.2004.01.004

  66. D. d’Enterria, R. Engel, T. Pierog, S. Ostapchenko, K. Werner, Astropart. Phys. 35, 98 (2011). https://doi.org/10.1016/j.astropartphys.2011.05.002

  67. M. Boezio, E. Mocchiutti, Astropart. Phys. 39–40, 95 (2012). https://doi.org/10.1016/j.astropartphys.2012.05.007

  68. Y.S. Yoon et al., Astrophys. J. 728, 122 (2011). https://doi.org/10.1088/0004-637X/728/2/122

  69. E. Seo, in PoS ICRC2015, vol. 574 (2015)

    Google Scholar 

  70. M. Xu, Nucl. Part. Phys. Proc. 279–281, 161 (2016). https://doi.org/10.1016/j.nuclphysbps.2016.10.023

  71. J.R. Hoerandel, Astropart. Phys. 19, 193 (2003). https://doi.org/10.1016/S0927-6505(02)00198-6

  72. T.K. Gaisser, T. Stanev, S. Tilav, Front. Phys. (Beijing) 8, 748 (2013). https://doi.org/10.1007/s11467-013-0319-7

  73. W.D. Apel et al., Phys. Rev. Lett. 107, 171104 (2011). https://doi.org/10.1103/PhysRevLett.107.171104

  74. N. Budnev et al., Astropart. Phys. 50–52, 18 (2013). https://doi.org/10.1016/j.astropartphys.2013.09.006

  75. V.V. Prosin et al., Nucl. Instrum. Meth. A756, 94 (2014). https://doi.org/10.1016/j.nima.2013.09.018

  76. M.G. Aartsen et al., Phys. Rev. D 88(4), 042004 (2013). https://doi.org/10.1103/PhysRevD.88.042004

  77. K.H. Kampert, M. Unger, Astropart. Phys. 35, 660 (2012). https://doi.org/10.1016/j.astropartphys.2012.02.004

  78. W.D. Apel et al., Astropart. Phys. 47, 54 (2013). https://doi.org/10.1016/j.astropartphys.2013.06.004

  79. W.D. Apel et al., Adv. Space Res. 53, 1456 (2014). https://doi.org/10.1016/j.asr.2013.05.008

  80. M. Aglietta et al., Astropart. Phys. 21, 223 (2004). https://doi.org/10.1016/j.astropartphys.2004.01.005

  81. M. Ambrosio et al., Phys. Rev. D 56, 1418 (1997). https://doi.org/10.1103/PhysRevD.56.1418

  82. M. Amenomori et al., Phys. Lett. B 632, 58 (2006). https://doi.org/10.1016/j.physletb.2005.10.048

  83. M. Amenomori et al., Adv. Space Res. 47, 629 (2011). https://doi.org/10.1016/j.asr.2010.08.029

  84. M.A.K. Glasmacher et al., Astropart. Phys. 12, 1 (1999). https://doi.org/10.1016/S0927-6505(99)00076-6

  85. S. Ogio et al., Astrophys. J. 612, 268 (2004). https://doi.org/10.1086/422510

  86. H. Tokuno et al., Astropart. Phys. 29, 453 (2008). https://doi.org/10.1016/j.astropartphys.2008.05.001

  87. H.T. Freudenreich, A.I. Mincer, D. Berley, J.A. Goodman, S. Tonwar, A. Wrotniak, G.B. Yodh, R.W. Ellsworth, Phys. Rev. D 41, 2732 (1990). https://doi.org/10.1103/PhysRevD.41.2732

  88. I. De Mitri, A. D’Amone, L. Perrone, A. Surdo, in PoS ICRC2015, vol. 366 (2016)

    Google Scholar 

  89. S.M. Mari, P. Montini, EPJ Web Conf. 121, 03008 (2016). https://doi.org/10.1051/epjconf/201612103008

  90. G. Di Sciascio, R. Iuppa, in Homage to the Discovery of Cosmic Rays (Nova Science Publishers, New York, 2013). arXiv:1407.2144

    Google Scholar 

  91. O. Wollan, Rev. Mod. Phys. 11, 11 (1939)

    Article  Google Scholar 

  92. M. Amenomori et al., Astropart. Phys. 36, 237 (2012). https://doi.org/10.1016/j.astropartphys.2012.06.005

  93. A.A. Abdo et al., Astrophys. J. 698, 2121 (2009). https://doi.org/10.1088/0004-637X/698/2/2121

  94. B. Bartoli et al., Astrophys. J. 809(1), 90 (2015). https://doi.org/10.1088/0004-637X/809/1/90

  95. M.G. Aartsen et al., Astrophys. J. 826(2), 220 (2016). https://doi.org/10.3847/0004-637X/826/2/220

  96. A.H. Compton, I.A. Getting, Phys. Rev. 47(11), 817 (1935). https://doi.org/10.1103/PhysRev.47.817

  97. P. Mertsch, S. Funk, Phys. Rev. Lett. 114(2), 021101 (2015). https://doi.org/10.1103/PhysRevLett. 114.021101

  98. A.D. Erlykin, A.W. Wolfendale, Astropart. Phys. 25, 183 (2006). https://doi.org/10.1016/j.astropartphys.2006.01.003

  99. V.S. Ptuskin, F.C. Jones, E.S. Seo, R. Sina, Adv. Space Res. 37, 1909 (2006). https://doi.org/10.1016/j.asr.2005.08.036

  100. M. Amenomori, Science 314, 439 (2006). https://doi.org/10.1126/SCIENCE.1131702

  101. A.A. Abdo et al., Phys. Rev. Lett. 101, 221101 (2008). https://doi.org/10.1103/PhysRevLett.101.221101

  102. B. Bartoli et al., Phys. Rev. D 88(8), 082001 (2013). https://doi.org/10.1103/PhysRevD.88.082001

  103. A.U. Abeysekara et al., Astrophys. J. 796(2), 108 (2014). https://doi.org/10.1088/0004-637X/796/2/108

  104. G. Giacinti, G. Sigl, Phys. Rev. Lett. 109(7), 071101 (2012). https://doi.org/10.1103/PhysRevLett.109.071101

  105. M. Ahlers, Phys. Rev. Lett. 112(2), 021101 (2014). https://doi.org/10.1103/PhysRevLett. 112.021101

  106. A. Aab et al., Phys. Rev. Lett. 116(24), 241101 (2016). https://doi.org/10.1103/PhysRevLett. 116.241101

  107. S. Vernetto, J. Phys. Conf. Ser. 718(5), 052043 (2016). https://doi.org/10.1088/1742-6596/718/5/052043

  108. R.U. Abbasi et al., Phys. Rev. Lett. 100, 101101 (2008). https://doi.org/10.1103/PhysRevLett.100.101101

  109. M. Takeda et al., Astropart. Phys. 19, 447 (2003). https://doi.org/10.1016/S0927-6505(02)00243-8

  110. T. Abu-Zayyad et al., Phys. Rev. Lett. 84, 4276 (2000). https://doi.org/10.1103/PhysRevLett.84.4276

  111. P. Abreu et al., Astropart. Phys. 34, 368 (2011). https://doi.org/10.1016/j.astropartphys.2010.10.001

  112. A. Aab et al., Nucl. Instrum. Meth. A798, 172 (2015). https://doi.org/10.1016/j.nima.2015.06.058

  113. T. Abu-Zayyad et al., Nucl. Instrum. Meth. A689, 87 (2012). https://doi.org/10.1016/j.nima.2012.05.079

  114. E. Zas, J. Phys. Conf. Ser. 632(1), 012104 (2015). https://doi.org/10.1088/1742-6596/632/1/012104

  115. V. Verzi, Rapporteur report at ICRC 2015 (2015)

    Google Scholar 

  116. J. Abraham et al., Phys. Rev. Lett. 101, 061101 (2008). https://doi.org/10.1103/PhysRevLett.101.061101

  117. T. Abu-Zayyad et al., Astrophys. J. 768, L1 (2013). https://doi.org/10.1088/2041-8205/768/1/L1

  118. The Pierre Auger Observatory: Contributions to the 34th International Cosmic Ray Conference (ICRC 2015)

    Google Scholar 

  119. A. Aab et al., Astrophys. J. 802(2), 111 (2015). https://doi.org/10.1088/0004-637X/802/2/111

  120. P. Abreu et al., JCAP 1302, 026 (2013). https://doi.org/10.1088/1475-7516/2013/02/026

  121. A. Aab et al., Phys. Rev. D 90(12), 122006 (2014). https://doi.org/10.1103/PhysRevD.90.122006

  122. A. Aab et al., Astrophys. J. 804(1), 15 (2015). https://doi.org/10.1088/0004-637X/804/1/15

  123. R.U. Abbasi et al., Astrophys. J. 790, L21 (2014). https://doi.org/10.1088/2041-8205/790/2/L21

  124. M.G. Aartsen et al., JCAP 1601(01), 037 (2016). https://doi.org/10.1088/1475-7516/2016/01/037

  125. M. Kachelriess, P.D. Serpico, Phys. Lett. B 640, 225 (2006). https://doi.org/10.1016/j.physletb.2006.08.006

  126. P. Abreu et al., Astropart. Phys. 34, 627 (2011). https://doi.org/10.1016/j.astropartphys.2010.12.007

  127. A. Aab et al., Astrophys. J. 794(2), 172 (2014). https://doi.org/10.1088/0004-637X/794/2/172

  128. R.U. Abbasi, et al., Pierre Auger and Telescope Array Collaborations, in Joint Contributions to the 34th International Cosmic Ray Conference (ICRC 2015) (2015), arXiv:1511.02103

  129. A. Aab, et al. (2016), arXiv:1604.03637

  130. H. Sagawa, JPS Conf. Proc. 9, 010014 (2016). https://doi.org/10.7566/JPSCP.9.010014

  131. T. Nonaka, M. Takamura, K. Honda, J.N. Matthews, S. Ogio, N. Sakurai, H. Sagawa, B.T. Stokes, M. Tsujimoto, K. Yashiro, JPS Conf. Proc. 9, 010013 (2016). https://doi.org/10.7566/JPSCP.9.010013

  132. F. Fenu (2017), arXiv:1703.01875

  133. T. Ebisuzaki, G. Medina-Tanco, A. Santangelo, Adv. Space Res. 53, 1499 (2014). https://doi.org/10.1016/j.asr.2013.11.056

  134. M. Potgieter, Living Rev. Solar Phys. 10, 3 (2013). https://doi.org/10.12942/lrsp-2013-3

  135. E.C. Stone, A.C. Cummings, F.B. McDonald, B.C. Heikkila, N. Lal, W.R. Webber, Science 341, 150 (2013). https://doi.org/10.1126/science.1236408

  136. J. Skilling, MNRAS 173, 255 (1975). https://doi.org/10.1093/mnras/173.2.255

  137. R.M. Kulsrud, C.J. Cesarsky, ApJ Lett. 8, 189 (1971)

    ADS  Google Scholar 

  138. Y. Zhou, W.H. Matthaeus, J. Geoph. Res. 95, 14881 (1990). https://doi.org/10.1029/JA095iA09p14881

  139. Y. Zhou, W.H. Matthaeus, JGR 95, 10291 (1990). https://doi.org/10.1029/JA095iA07p10291

  140. J. Skilling, Astrophys. J. 170, 265 (1971). https://doi.org/10.1086/151210

  141. J.A. Holmes, MNRAS 170, 251 (1975). https://doi.org/10.1093/mnras/170.2.251

  142. K.M. Ferriere, Rev. Mod. Phys. 73, 1031 (2001). https://doi.org/10.1103/RevModPhys.73.1031

  143. V.S. Ptuskin, V.N. Zirakashvili, A&A 403, 1 (2003). https://doi.org/10.1051/0004-6361:20030323

  144. R. Aloisio, P. Blasi, P. Serpico, Astron. Astrophys. 583, A95 (2015). https://doi.org/10.1051/0004-6361/201526877

  145. F. Acero et al., Astrophys. J. Suppl. 223(2), 26 (2016). https://doi.org/10.3847/0067-0049/223/2/26

  146. R.z. Yang, F. Aharonian, C. Evoli (2016), arXiv:1602.04710

  147. F.W. Stecker, F.C. Jones, Astrophys. J. 217, 843 (1977). https://doi.org/10.1086/155631

  148. M. Ackermann et al., Astrophys. J. 726, 81 (2011). https://doi.org/10.1088/0004-637X/726/2/81

  149. M. Ackermann et al., Astron. Astrophys. 538, A71 (2012). https://doi.org/10.1051/0004-6361/201117539

  150. V.S. Berezinsky, S.V. Bulanov, V.A. Dogiel, V.L. Ginzburg, V.S. Ptuskin, Astrophysics of Cosmic Rays (Amsterdam, 1990) 534 p

    Google Scholar 

  151. J.B.G.M. Bloemen, V.A. Dogiel, V.L. Dorman, V.S. Ptuskin, A&A 267, 372 (1993)

    ADS  Google Scholar 

  152. A.W. Strong, I.V. Moskalenko, O. Reimer, S. Digel, R. Diehl, Astron. Astrophys. 422, L47 (2004). https://doi.org/10.1051/0004-6361:20040172

  153. A. Erlykin, A. Wolfendale, V. Dogiel, Adv. Space Res. 57, 519 (2016). https://doi.org/10.1016/j.asr.2015.10.010

  154. C. Evoli, D. Gaggero, D. Grasso, L. Maccione, Phys. Rev. Lett. 108, 211102 (2012). https://doi.org/10.1103/PhysRevLett.108.211102

  155. D. Gaggero, A. Urbano, M. Valli, P. Ullio, Phys. Rev. D 91(8), 083012 (2015). https://doi.org/10.1103/PhysRevD.91.083012

  156. S. Recchia, P. Blasi, G. Morlino (2015), arXiv:1604.07682

  157. R.A. Crain, V.R. Eke, C.S. Frenk, A. Jenkins, I.G. McCarthy, J.F. Navarro, F.R. Pearce, Mon. Not. R. Astron. Soc. 377, 41 (2007). https://doi.org/10.1111/j.1365-2966.2007.11598.x

  158. G. Stinson, C. Brook, A.V. Maccio, J. Wadsley, T.R. Quinn, H.M.P. Couchman, Mon. Not. R. Astron. Soc. 428, 129 (2013). https://doi.org/10.1093/mnras/sts028

  159. P.M.W. Kalberla, G. Westphalen, U. Mebold, D. Hartmann, W.B. Burton, A&A 332, L61 (1998)

    ADS  Google Scholar 

  160. P.M.W. Kalberla, L. Dedes, Astron. Astrophys. 487, 951 (2008). https://doi.org/10.1051/0004-6361:20079240

  161. M.J. Miller, J.N. Bregman, Astrophys. J. 770, 118 (2013). https://doi.org/10.1088/0004-637X/770/2/118

  162. S.L. Snowden, M.J. Freyberg, P.P. Plucinsky, J.H.M.M. Schmitt, J. Truemper, W. Voges, R.J. Edgar, D. McCammon, W.T. Sanders, ApJ 454, 643 (1995). https://doi.org/10.1086/176517

  163. D. Breitschwerdt, T. Schmutzler, Nature 371, 774 (1994). https://doi.org/10.1038/371774a0

  164. D. Breitschwerdt, T. Schmutzler, Astron. Astrophys. 347, 650 (1999)

    ADS  Google Scholar 

  165. J.E. Everett, E.G. Zweibel, R.A. Benjamin, D. McCammon, L. Rocks, J.S. Gallagher, Astrophys. J. 674, 258 (2008). https://doi.org/10.1086/524766

  166. R.A. Chevalier, A.W. Clegg, Nature 317, 44 (1985). https://doi.org/10.1038/317044a0

  167. N. Scoville, J. Korean Astronom. Soc. 36, 167 (2003). https://doi.org/10.5303/JKAS.2003.36.3.167

  168. N. Murray, E. Quataert, T.A. Thompson, Astrophys. J. 618, 569 (2005). https://doi.org/10.1086/426067

  169. S. Veilleux, G. Cecil, J. Bland-Hawthorn, Ann. Rev. Astron. Astrophys. 43, 769 (2005). https://doi.org/10.1146/annurev.astro.43.072103.150610

  170. K.S. Cheng, D.O. Chernyshov, V.A. Dogiel, C.M. Ko, W.H. Ip, Astrophys. J. 731, L17 (2011). https://doi.org/10.1088/2041-8205/731/1/L17

  171. K. Zubovas, A.R. King, S. Nayakshin, Mon. Not. R. Astron. Soc. 415, 21 (2011). https://doi.org/10.1111/j.1745-3933.2011.01070.x

  172. B.C. Lacki, Mon. Not. R. Astron. Soc. (2013). https://doi.org/10.1093/mnrasl/slu107

  173. F.M. Ipavich, Astrophys. J. 196, 107 (1975). https://doi.org/10.1086/153397

  174. D. Breitschwerdt, J.F. McKenzie, H.J. Voelk, A&A 245, 79 (1991)

    ADS  Google Scholar 

  175. D. Breitschwerdt, J.F. McKenzie, H.J. Voelk, Astron. Astrophys. (ISSN 0004-6361) 269, 54 (1993)

    Google Scholar 

  176. M. Uhlig, C. Pfrommer, M. Sharma, B.B. Nath, T.A. Ensslin, V. Springel, Mon. Not. R. Astron. Soc. 423, 2374 (2012). https://doi.org/10.1111/j.1365-2966.2012.21045.x

  177. C.M. Booth, O. Agertz, A.V. Kravtsov, N.Y. Gnedin, Astrophys. J. 777, L16 (2013). https://doi.org/10.1088/2041-8205/777/1/L16

  178. M. Salem, G.L. Bryan, Mon. Not. R. Astron. Soc. 437(4), 3312 (2014). https://doi.org/10.1093/mnras/stt2121

  179. P. Girichidis, T. Naab, S. Walch, M. Hanasz, M.M. Mac Low, J.P. Ostriker, A. Gatto, T. Peters, R. Wünsch, S.C.O. Glover, R.S. Klessen, P.C. Clark, C. Baczynski, ApJ Lett. 816, L19 (2016). https://doi.org/10.3847/2041-8205/816/2/L19

  180. T. Peters, P. Girichidis, A. Gatto, T. Naab, S. Walch, R. Wnsch, S.C.O. Glover, P.C. Clark, R.S. Klessen, C. Baczynski. Astrophys. J. 813(2), L27 (2015). https://doi.org/10.1088/2041-8205/813/2/L27

  181. M. Ruszkowski, H.Y.K. Yang, E. Zweibel (2016), arXiv:1602.04856

  182. V.S. Ptuskin, H.J. Voelk, V.N. Zirakashvili, D. Breitschwerdt, A&A 321, 434 (1997)

    ADS  Google Scholar 

  183. S. Recchia, P. Blasi, G. Morlino, MNRAS 462, 4227 (2016). https://doi.org/10.1093/mnras/stw1966

  184. P.D. Serpico, in PoS ICRC2015, vol. 009 (2016)

    Google Scholar 

  185. M. di Mauro, F. Donato, A. Goudelis, P.D. Serpico, PRD 90(8), 085017 (2014). https://doi.org/10.1103/PhysRevD.90.085017

  186. O. Adriani et al., Phys. Rev. Lett. 106, 201101 (2011). https://doi.org/10.1103/PhysRevLett.106.201101

  187. M. Aguilar, D. Aisa, A. Alvino, G. Ambrosi, K. Andeen, L. Arruda, N. Attig, P. Azzarello, A. Bachlechner, F. Barao et al., Phys. Rev. Lett. 113(12), 121102 (2014). https://doi.org/10.1103/PhysRevLett.113.121102

  188. P. Mertsch, S. Sarkar, Phys. Rev. Lett. 103, 081104 (2009). https://doi.org/10.1103/PhysRevLett.103.081104

  189. E. Amato, Int. J. Mod. Phys. Conf. Ser. 28, 1460160 (2014). https://doi.org/10.1142/S2010194514601604

  190. F.A. Aharonian, A.M. Atoyan, H.J. Voelk, A&A 294, L41 (1995)

    ADS  Google Scholar 

  191. P. Blasi, E. Amato, Astrophys. Space Sci. Proc. 623–641 (2011). https://doi.org/10.1007/978-3-642-17251-9_50

  192. T. Linden, S. Profumo, Astrophys. J. 772, 18 (2013). https://doi.org/10.1088/0004-637X/772/1/18

  193. R. Cowsik, B. Burch, PRD 82(2), 023009 (2010). https://doi.org/10.1103/PhysRevD.82.023009

  194. R. Cowsik, T. Madziwa-Nussinov, Ap. J. 827, 119 (2016). https://doi.org/10.3847/0004-637X/827/2/119

  195. M. D’Angelo, P. Blasi, E. Amato, PRD 94(8), 083003 (2016). https://doi.org/10.1103/PhysRevD.94.083003

  196. G.F. Krymskii, Akademiia Nauk SSSR Doklady 234, 1306 (1977)

    ADS  Google Scholar 

  197. R.D. Blandford, J.P. Ostriker, Astrophys. J. 221, L29 (1978). https://doi.org/10.1086/182658

  198. W.I. Axford, E. Leer, G. Skadron, Int. Cosm. Ray Conf. 11, 132 (1977)

    Google Scholar 

  199. A.R. Bell, Mon. Not. R. Astron. Soc. 182, 443 (1978)

    Article  ADS  Google Scholar 

  200. M. Malkov, L.O. Drury, Rep. Prog. Phys. 64(4), 429 (2001). https://doi.org/10.1088/0034-4885/64/4/201

  201. L.O. Drury, J.H. Voelk, ApJ 248, 344 (1981). https://doi.org/10.1086/159159

  202. W.I. Axford, E. Leer, J.F. McKenzie, A&A 111, 317 (1982)

    ADS  Google Scholar 

  203. E.G. Berezhko, D.C. Ellison, ApJ 526, 385 (1999). https://doi.org/10.1086/307993

  204. E.G. Berezhko, V.K. Elshin, L.T. Ksenofontov, Astropart. Phys. 2, 215 (1994). https://doi.org/10.1016/0927-6505(94)90043-4

  205. E.G. Berezhko, H.J. Volk, Astropart. Phys. 7, 183 (1997). https://doi.org/10.1016/S0927-6505(97)00016-9

  206. M.A. Malkov, Astrophys. J. 511, L53 (1999). https://doi.org/10.1086/311825

  207. P. Blasi, Astropart. Phys. 16, 429 (2002). https://doi.org/10.1016/S0927-6505(01)00127-X

  208. J. Ballet, Adv. Space Res. 37, 1902 (2006). https://doi.org/10.1016/j.asr.2005.03.047

  209. D. Caprioli, E. Amato, P. Blasi, Astropart. Phys. 33, 160 (2010). https://doi.org/10.1016/j.astropartphys.2010.01.002

  210. P. Mertsch, S. Funk, Phys. Rev. Lett. 114(2), 021101 (2015). https://doi.org/10.1103/PhysRevLett.114.021101

  211. D. Caprioli, JCAP 1105, 026 (2011). https://doi.org/10.1088/1475-7516/2011/05/026

  212. F. Acero et al., Astrophys. J. Suppl. 224(1), 8 (2016). https://doi.org/10.3847/0067-0049/224/1/8

  213. E.G. Berezhko, L.T. Ksenofontov, H.J. Vlk, Astrophys. J. 763, 14 (2013). https://doi.org/10.1088/0004-637X/763/1/14

  214. P. Blasi, G. Morlino, R. Bandiera, E. Amato, D. Caprioli, Astrophys. J. 755, 121 (2012). https://doi.org/10.1088/0004-637X/755/2/121

  215. G. Morlino, P. Blasi, Astron. Astrophys. 589, A7 (2016). https://doi.org/10.1051/0004-6361/201527761

  216. D. Caprioli, JCAP 1207, 038 (2012). https://doi.org/10.1088/1475-7516/2012/07/038

  217. G. Morlino, D. Caprioli, Astron. Astrophys. 538, A81 (2012). https://doi.org/10.1051/0004-6361/201117855

  218. K.M. Schure, A.R. Bell, Mon. Not. R. Astron. Soc. 435, 1174 (2013). https://doi.org/10.1093/mnras/stt1371

  219. P.O. Lagage, C.J. Cesarsky, Astron. Astrophys. 118, 223 (1983)

    ADS  Google Scholar 

  220. J. Giacalone, J.R. Jokipii, Astrophys. J. 663, L41 (2007). https://doi.org/10.1086/519994

  221. A.R. Bell, Mon. Not. R. Astron. Soc. 353, 550 (2004). https://doi.org/10.1111/j.1365-2966.2004.08097.x

  222. D. Caprioli, in PoS ICRC2015, vol. 008 (2015)

    Google Scholar 

  223. D. Caprioli, A. Spitkovsky, Astrophys. J. 783, 91 (2014). https://doi.org/10.1088/0004-637X/783/2/91

  224. D. Caprioli, A. Spitkovsky, Astrophys. J. 794(1), 46 (2014). https://doi.org/10.1088/0004-637X/794/1/46

  225. E. Amato, P. Blasi, Mon. Not. R. Astron. Soc. 392, 1591 (2009). https://doi.org/10.1111/j.1365-2966.2008.14200.x

  226. D. Caprioli, A.R. Pop, A. Spitkovsky, Astrophys. J. 798(2), L28 (2015). https://doi.org/10.1088/2041-8205/798/2/L28

  227. J. Park, D. Caprioli, A. Spitkovsky, Phys. Rev. Lett. 114(8), 085003 (2015). https://doi.org/10.1103/PhysRevLett.114.085003

  228. A. Abramowski et al., Nature 531, 476 (2016). https://doi.org/10.1038/nature17147

  229. G. Morlino, P. Blasi, R. Bandiera, E. Amato, D. Caprioli, Astrophys. J. 768, 148 (2013). https://doi.org/10.1088/0004-637X/768/2/148

  230. G. Morlino, R. Bandiera, P. Blasi, E. Amato, Astrophys. J. 760, 137 (2012). https://doi.org/10.1088/0004-637X/760/2/137

  231. G. Morlino, P. Blasi, R. Bandiera, E. Amato, Astron. Astrophys. 558, A25 (2013). https://doi.org/10.1051/0004-6361/201322006

  232. G. Morlino, P. Blasi, R. Bandiera, E. Amato, Astron. Astrophys. 562, A141 (2014). https://doi.org/10.1051/0004-6361/201322986

  233. G. Morlino, P. Blasi, R. Bandiera, E. Amato, Astron. Astrophys. 557, A142 (2013). https://doi.org/10.1051/0004-6361/201322161

  234. P. Ghavamian, S.J. Schwartz, J. Mitchell, A. Masters, J.M. Laming, Space Sci. Rev. 178, 633 (2013). https://doi.org/10.1007/s11214-013-9999-0

  235. R. Aloisio, V. Berezinsky, A. Gazizov, Astropart. Phys. 39–40, 129 (2012). https://doi.org/10.1016/j.astropartphys.2012.09.007

  236. A. Franceschini, G. Rodighiero, M. Vaccari, Astron. Astrophys. 487, 837 (2008). https://doi.org/10.1051/0004-6361:200809691

  237. F.W. Stecker, M. Malkan, S. Scully, Astrophys. J. 658, 1392 (2007). https://doi.org/10.1086/511738

  238. F.W. Stecker, M. Malkan, S. Scully, Astrophys. J. 648, 774 (2006). https://doi.org/10.1086/506188

  239. T.M. Kneiske, T. Bretz, K. Mannheim, D. Hartmann, Astron. Astrophys. 413, 807 (2004). https://doi.org/10.1051/0004-6361:20031542

  240. R. Aloisio, D. Boncioli, A. di Matteo, A.F. Grillo, S. Petrera, F. Salamida, JCAP 1510(10), 006 (2015). https://doi.org/10.1088/1475-7516/2015/10/006

  241. R. Aloisio, V. Berezinsky, S. Grigorieva, Astropart. Phys. 41, 73 (2013). https://doi.org/10.1016/j.astropartphys.2012.07.010

  242. R. Aloisio, V. Berezinsky, S. Grigorieva, Astropart. Phys. 41, 94 (2013). https://doi.org/10.1016/j.astropartphys.2012.06.003

  243. A.A. Penzias, R.W. Wilson, Astrophys. J. 142, 419 (1965). https://doi.org/10.1086/148307

  244. K. Greisen, Phys. Rev. Lett. 16, 748 (1966). https://doi.org/10.1103/PhysRevLett.16.748

  245. G. Zatsepin, V. Kuzmin, JETP Lett. 4, 78 (1966)

    ADS  Google Scholar 

  246. A.M. Hillas, Phys. Lett. A 24, 677 (1967)

    Article  ADS  Google Scholar 

  247. G.R. Blumenthal, Phys. Rev. D 1, 1596 (1970). https://doi.org/10.1103/PhysRevD.1.1596

  248. V. Berezinsky, G. Zatsepin, Phys. Lett. B 28, 423 (1969). https://doi.org/10.1016/0370-2693(69)90341-4

  249. F. Stecker, Astrophys. Space Sci. 20, 47 (1973). https://doi.org/10.1007/BF00645585

  250. A. Strong, A. Wolfendale, J. Wdowczy, Nature 241, 109 (1973)

    Article  ADS  Google Scholar 

  251. V. Berezinsky, A.Y. Smirnov, Astrophys. Space Sci. 32, 461 (1975). https://doi.org/10.1007/BF00643157

  252. F.W. Stecker, Phys. Rev. Lett. 21, 1016 (1968). https://doi.org/10.1103/PhysRevLett.21.1016

  253. V. Berezinsky, A. Gazizov, S. Grigorieva, Phys. Rev. D 74, 043005 (2006). https://doi.org/10.1103/PhysRevD.74.043005

  254. J. Puget, F. Stecker, J. Bredekamp, Astrophys. J. 205, 638 (1976). https://doi.org/10.1086/154321

  255. D. Allard, E. Parizot, E. Khan, S. Goriely, A. Olinto, Astron. Astrophys. 443, L29 (2005). https://doi.org/10.1051/0004-6361:200500199

  256. P.A.R. Ade, et al., Planck collaboration, eprint 1502.01589 (2015)

    Google Scholar 

  257. J. Linsley, in Proceedings of 8th ICRC (Jaipur 1963), vol. 4, p. 77 (1963)

    Google Scholar 

  258. R.U. Abbasi et al., Astropart. Phys. 68, 27 (2015). https://doi.org/10.1016/j.astropartphys.2015.02.008

  259. R.U. Abbasi et al., Phys. Rev. Lett. 92, 151101 (2004). https://doi.org/10.1103/PhysRevLett.92.151101

  260. V. Egorova et al., [Yakutsk Collaboration] Nucl. Phys. Proc. Suppl. 3, 136 (2004)

    Google Scholar 

  261. K. Shinozaki et al., [AGASA Collaboration] Nucl. Phys. Proc. Suppl. 3, 151 (2006)

    Google Scholar 

  262. M. Honda et al., [Akeno Collaboration] Phys. Rev. D 70, 525 (1993)

    Google Scholar 

  263. C.C.H. Jui, J. Phys. Conf. Ser. 404, 012037 (2012). https://doi.org/10.1088/1742-6596/404/1/012037

  264. R. Aloisio, V. Berezinsky, P. Blasi, A. Gazizov, S. Grigorieva, B. Hnatyk, Astropart. Phys. 27, 76 (2007). https://doi.org/10.1016/j.astropartphys.2006.09.004

  265. V. Berezinsky, A.Z. Gazizov, S.I. Grigorieva, Phys. Lett. B 612, 147 (2005). https://doi.org/10.1016/j.physletb.2005.02.058

  266. R. Aloisio, V. Berezinsky, P. Blasi, S. Ostapchenko, Phys. Rev. D 77, 025007 (2008). https://doi.org/10.1103/PhysRevD.77.025007

  267. D. De Marco, T. Stanev, Phys. Rev. D 72, 081301 (2005). https://doi.org/10.1103/PhysRevD.72.081301

  268. M. Kachelriess, D.V. Semikoz, Phys. Lett. B 634, 143 (2006). https://doi.org/10.1016/j.physletb.2006.01.009

  269. R. Aloisio, V.S. Berezinsky, Astrophys. J. 625, 249 (2005). https://doi.org/10.1086/429615

  270. R. Aloisio, V. Berezinsky, A. Gazizov, Astropart. Phys. 34, 620 (2011). https://doi.org/10.1016/j.astropartphys.2010.12.008

  271. A.M. Taylor, Astropart. Phys. 54, 48 (2014). https://doi.org/10.1016/j.astropartphys.2013.11.006

  272. A. Aab et al., JCAP 1704(04), 038 (2017). https://doi.org/10.1088/1475-7516/2017/04/038

  273. N. Globus, D. Allard, E. Parizot, Phys. Rev. D 92(2), 021302 (2015). https://doi.org/10.1103/PhysRevD.92.021302

  274. P. Abreu et al., Astrophys. J. 762, L13 (2012). https://doi.org/10.1088/2041-8205/762/1/L13

  275. G. Giacinti, M. Kachelriess, D.V. Semikoz, G. Sigl, JCAP 1207, 031 (2012). https://doi.org/10.1088/1475-7516/2012/07/031

  276. N. Globus, D. Allard, R. Mochkovitch, E. Parizot, Mon. Not. R. Astron. Soc. 451(1), 751 (2015). https://doi.org/10.1093/mnras/stv893

  277. M. Unger, G.R. Farrar, L.A. Anchordoqui, Phys. Rev. D 92(12), 123001 (2015). https://doi.org/10.1103/PhysRevD.92.123001

  278. G.B. Gelmini, O. Kalashev, D.V. Semikoz, JCAP 1201, 044 (2012). https://doi.org/10.1088/1475-7516/2012/01/044

  279. H. Yuksel, M.D. Kistler, J.F. Beacom, A.M. Hopkins, Astrophys. J. 683, L5 (2008). https://doi.org/10.1086/591449

  280. X.Y. Wang, R.Y. Liu, F. Aharnonian, Astrophys. J. 736, 112 (2011). https://doi.org/10.1088/0004-637X/736/2/112

  281. G. Hasinger, T. Miyaji, M. Schmidt, Astron. Astrophys. 441, 417 (2005). https://doi.org/10.1051/0004-6361:20042134

  282. M. Ahlers, L.A. Anchordoqui, S. Sarkar, Phys. Rev. D 79, 083009 (2009). https://doi.org/10.1103/PhysRevD.79.083009

  283. R. Engel, D. Heck, T. Pierog, Ann. Rev. Nucl. Part. Sci. 61, 467 (2011). https://doi.org/10.1146/annurev.nucl.012809.104544

  284. T. Pierog, K. Werner, Phys. Rev. Lett. 101, 171101 (2008). https://doi.org/10.1103/PhysRevLett.101.171101

  285. E.J. Ahn, R. Engel, T.K. Gaisser, P. Lipari, T. Stanev, Phys. Rev. D 80, 094003 (2009). https://doi.org/10.1103/PhysRevD.80.094003

  286. N. Kalmykov, S. Ostapchenko, A. Pavlov, Nucl. Phys. Proc. Suppl. 52B, 17 (1997)

    Article  ADS  Google Scholar 

  287. S. Ostapchenko, Phys. Rev. D 74, 014026 (2006). https://doi.org/10.1103/PhysRevD.74.014026

  288. R. Engel, D. Seckel, T. Stanev, Phys. Rev. D 64, 093010 (2001). https://doi.org/10.1103/PhysRevD.64.093010

  289. O.E. Kalashev, V.A. Kuzmin, D.V. Semikoz, G. Sigl, Phys. Rev. D 66, 063004 (2002). https://doi.org/10.1103/PhysRevD.66.063004

  290. D. Hooper, A. Taylor, S. Sarkar, Astropart. Phys. 23, 11 (2005). https://doi.org/10.1016/j.astropartphys.2004.11.002

  291. D. Seckel, T. Stanev, Phys. Rev. Lett. 95, 141101 (2005). https://doi.org/10.1103/PhysRevLett.95.141101

  292. D. De Marco, T. Stanev, F.W. Stecker, Phys. Rev. D 73, 043003 (2006). https://doi.org/10.1103/PhysRevD.73.043003

  293. D. Allard, M. Ave, N. Busca, M. Malkan, A. Olinto et al., JCAP 0609, 005 (2006). https://doi.org/10.1088/1475-7516/2006/09/005

  294. L.A. Anchordoqui, H. Goldberg, D. Hooper, S. Sarkar, A.M. Taylor, Phys. Rev. D 76, 123008 (2007). https://doi.org/10.1103/PhysRevD.76.123008

  295. H. Takami, K. Murase, S. Nagataki, K. Sato, Astropart. Phys. 31, 201 (2009). https://doi.org/10.1016/j.astropartphys.2009.01.006

  296. K. Kotera, D. Allard, A.V. Olinto, JCAP 1010, 013 (2010). https://doi.org/10.1088/1475-7516/2010/10/013

  297. V. Berezinsky, A. Gazizov, M. Kachelriess, S. Ostapchenko, Phys. Lett. B 695, 13 (2011). https://doi.org/10.1016/j.physletb.2010.11.019

  298. T. Stanev, Comptes Rendus Physique 15, 349 (2014). https://doi.org/10.1016/j.crhy.2014.02.013

  299. V. Berezinsky, O. Kalashev (2016), arXiv:1603.03989

  300. M. Aartsen et al., Science 342, 1242856 (2013). https://doi.org/10.1126/science.1242856

  301. M. Aartsen et al., Phys. Rev. Lett. 111, 021103 (2013). https://doi.org/10.1103/PhysRevLett.111.021103

  302. P. Abreu et al., Adv. High Energy Phys. 2013, 708680 (2013). https://doi.org/10.1155/2013/708680

  303. V. Berezinsky, P. Blasi, Phys. Rev. D 85, 123003 (2012). https://doi.org/10.1103/PhysRevD.85.123003

  304. T.J. Weiler, Phys. Rev. Lett. 49, 234 (1982). https://doi.org/10.1103/PhysRevLett. 49.234

  305. P. Gondolo, G. Gelmini, S. Sarkar, Nucl. Phys. B 392, 111 (1993). https://doi.org/10.1016/0550-3213(93)90199-Y

  306. G.R. Blumenthal, R.J. Gould, Rev. Mod. Phys. 42, 237 (1970). https://doi.org/10.1103/RevModPhys.42.237

  307. R.Y. Liu, A.M. Taylor, X.Y. Wang, F.A. Aharonian (2016), arXiv:1603.03223

  308. M. Ackermann et al., Astrophys. J. 799, 86 (2015). https://doi.org/10.1088/0004-637X/799/1/86

  309. M. Ackermann et al., Phys. Rev. Lett. 116(15), 151105 (2016). https://doi.org/10.1103/PhysRevLett.116.151105

  310. C. Ferrigno, P. Blasi, D. De Marco, Astropart. Phys. 23, 211 (2005). https://doi.org/10.1016/j.astropartphys.2004.04.013

  311. M. Ahlers, L.A. Anchordoqui, M.C. Gonzalez-Garcia, F. Halzen, S. Sarkar, Astropart. Phys. 34, 106 (2010). https://doi.org/10.1016/j.astropartphys.2010.06.003

  312. A.A. Abdo et al., Phys. Rev. Lett. 104, 101101 (2010). https://doi.org/10.1103/PhysRevLett.104.101101

  313. V. Berezinsky, A. Gazizov, O. Kalashev, Astropart. Phys. 84, 52 (2016). https://doi.org/10.1016/j.astropartphys.2016.08.007

  314. V. Berezinsky, M. Kachelriess, A. Vilenkin, Phys. Rev. Lett. 79, 4302 (1997). https://doi.org/10.1103/PhysRevLett.79.4302

  315. V. Berezinsky, P. Blasi, A. Vilenkin, Phys. Rev. D 58, 103515 (1998). https://doi.org/10.1103/PhysRevD.58.103515

  316. G. Sigl, S. Lee, P. Bhattacharjee, S. Yoshida, Phys. Rev. D 59, 043504 (1999). https://doi.org/10.1103/PhysRevD.59.043504

  317. R. Aloisio, V. Berezinsky, M. Kachelriess, Phys. Rev. D 69, 094023 (2004). https://doi.org/10.1103/PhysRevD.69.094023

  318. R. Aloisio, V. Berezinsky, M. Kachelriess, Phys. Rev. D 74, 023516 (2006). https://doi.org/10.1103/PhysRevD.74.023516

  319. R. Aloisio, S. Matarrese, A.V. Olinto, JCAP 1508(08), 024 (2015). https://doi.org/10.1088/1475-7516/2015/08/024

  320. S. Yoshida, M. Teshima, Prog. Theoret. Phys. 89, 833 (1993). https://doi.org/10.1143/PTP.89.833

  321. A.M. Taylor, J.A. Hinton, P. Blasi, M. Ave, Phys. Rev. Lett. 103, 051102 (2009). https://doi.org/10.1103/PhysRevLett.103.051102

  322. W. Essey, O.E. Kalashev, A. Kusenko, J.F. Beacom, Phys. Rev. Lett. 104, 141102 (2010). https://doi.org/10.1103/PhysRevLett.104.141102

  323. W. Essey, O. Kalashev, A. Kusenko, J.F. Beacom, Astrophys. J. 731, 51 (2011). https://doi.org/10.1088/0004-637X/731/1/51

  324. T. Stanev, Astrophys. J. 479, 290 (1997). https://doi.org/10.1086/303866

  325. D. Harari, S. Mollerach, E. Roulet, JHEP 02, 035 (2000). https://doi.org/10.1088/1126-6708/2000/02/035

  326. M. Prouza, R. Smida, Astron. Astrophys. 410, 1 (2003). https://doi.org/10.1051/0004-6361:20031281

  327. H. Yoshiguchi, S. Nagataki, K. Sato, Astrophys. J. 596, 1044 (2003). https://doi.org/10.1086/378201

  328. M. Kachelriess, P.D. Serpico, M. Teshima, Astropart. Phys. 26, 378 (2006). https://doi.org/10.1016/j.astropartphys.2006.08.004

  329. H. Takami, H. Yoshiguchi, K. Sato, Astrophys. J. 639, 803 (2006). https://doi.org/10.1086/499420. [Erratum: Astrophys. J. 653, 1584 (2006)]

  330. P.P. Kronberg, Rept. Prog. Phys. 57, 325 (1994). https://doi.org/10.1088/0034-4885/57/4/001

  331. D. Grasso, H.R. Rubinstein, Phys. Rept. 348, 163 (2001). https://doi.org/10.1016/S0370-1573(00)00110-1

  332. C.L. Carilli, G.B. Taylor, Ann. Rev. Astron. Astrophys. 40, 319 (2002). https://doi.org/10.1146/annurev.astro.40.060401.093852

  333. R.M. Kulsrud, E.G. Zweibel, Rep. Prog. Phys. 71, 0046091 (2008). https://doi.org/10.1088/0034-4885/71/4/046901

  334. R. Beck, A.I.P. Conf, Proc. 1381, 117 (2011). https://doi.org/10.1063/1.3635828

  335. D. Ryu, D.R.G. Schleicher, R.A. Treumann, C.G. Tsagas, L.M. Widrow, Space Sci. Rev. 166, 1 (2012). https://doi.org/10.1007/s11214-011-9839-z

  336. R. Durrer, A. Neronov, Astron. Astrophys. Rev. 21, 62 (2013). https://doi.org/10.1007/s00159-013-0062-7

  337. P. Blasi, S. Burles, A.V. Olinto, Astrophys. J. 514, L79 (1999). https://doi.org/10.1086/311958

  338. A. Elyiv, A. Neronov, D.V. Semikoz, Phys. Rev. D 80, 023010 (2009). https://doi.org/10.1103/PhysRevD.80.023010

  339. A. Neronov, D.V. Semikoz, Phys. Rev. D 80, 123012 (2009). https://doi.org/10.1103/PhysRevD.80.123012

  340. K. Dolag, M. Bartelmann, H. Lesch, Astron. Astrophys. 387, 383 (2002). https://doi.org/10.1051/0004-6361:20020241

  341. K. Dolag, D. Grasso, V. Springel, I. Tkachev, JCAP 0501, 009 (2005). https://doi.org/10.1088/1475-7516/2005/01/009

  342. G. Sigl, F. Miniati, T.A. Ensslin, Phys. Rev. D 70, 043007 (2004). https://doi.org/10.1103/PhysRevD.70.043007

  343. J. Donnert, K. Dolag, H. Lesch, E. Muller, Mon. Not. R. Astron. Soc. 392, 1008 (2009). https://doi.org/10.1111/j.1365-2966.2008.14132.x

  344. D. Ryu, H. Kang, J. Cho, S. Das, Science 320, 909 (2008). https://doi.org/10.1126/science.1154923

  345. R. Aloisio, V. Berezinsky, Astrophys. J. 612, 900 (2004). https://doi.org/10.1086/421869

  346. M. Lemoine, Phys. Rev. D 71, 083007 (2005). https://doi.org/10.1103/PhysRevD.71.083007

  347. R. Aloisio, V. Berezinsky, A. Gazizov, Astrophys. J. 693, 1275 (2009). https://doi.org/10.1088/0004-637X/693/2/1275

  348. S. Mollerach, E. Roulet, JCAP 1310, 013 (2013). https://doi.org/10.1088/1475-7516/2013/10/013

  349. P. Subedi, W. Sonsrettee, P. Blasi, D. Ruffolo, W.H. Matthaeus, D. Montgomery, P. Chuychai, P. Dmitruk, M. Wan, T.N. Parashar, R. Chhiber, Ap. J. 837, 140 (2017). https://doi.org/10.3847/1538-4357/aa603a

  350. S.L. Dubovsky, P.G. Tinyakov, I.I. Tkachev, Phys. Rev. Lett. 85, 1154 (2000). https://doi.org/10.1103/PhysRevLett. 85.1154

  351. Z. Fodor, S.D. Katz, Phys. Rev. D 63, 023002 (2001). https://doi.org/10.1103/PhysRevD.63.023002

  352. P. Blasi, D. De Marco, Astropart. Phys. 20, 559 (2004). https://doi.org/10.1016/j.astropartphys.2003.07.002

  353. M. Kachelriess, D. Semikoz, Astropart. Phys. 23, 486 (2005). https://doi.org/10.1016/j.astropartphys.2005.03.004

  354. K. Kotera, M. Lemoine, Phys. Rev. D 77, 023005 (2008). https://doi.org/10.1103/PhysRevD.77.023005

  355. K. Kotera, M. Lemoine, Phys. Rev. D 77, 123003 (2008). https://doi.org/10.1103/PhysRevD.77.123003

  356. S. Kalli, M. Lemoine, K. Kotera, Astron. Astrophys. 528, A109 (2011). https://doi.org/10.1051/0004-6361/201015688

  357. P. Blasi, E. Amato, M. D’Angelo, Phys. Rev. Lett. 115(12), 121101 (2015). https://doi.org/10.1103/PhysRevLett.115.121101

  358. A.M. Hillas, Ann. Rev. Astron. Astrophys. 22, 425 (1984). https://doi.org/10.1146/annurev.aa.22.090184.002233

  359. K. Kotera, A.V. Olinto, Ann. Rev. Astron. Astrophys. 49, 119 (2011). https://doi.org/10.1146/annurev-astro-081710-102620

  360. E. Waxman, Phys. Scr. T121, 147 (2005). https://doi.org/10.1088/0031-8949/2005/T121/022

  361. P. Blasi, EPJ Web Conf. 53, 01002 (2013). https://doi.org/10.1051/epjconf/20135301002

  362. J.H. Woo, C.M. Urry, Astrophys. J. 579, 530 (2002). https://doi.org/10.1086/342878

  363. L.H. Jiang, X.H. Fan, Z. Ivezic, G.T. Richards, D.P. Schneider, M.A. Strauss, B.C. Kelly, Astrophys. J. 656, 680 (2007). https://doi.org/10.1086/510831

  364. H. Kang, D. Ryu, T.W. Jones, Astrophys. J. 456, 422 (1996). https://doi.org/10.1086/176666

  365. H. Kang, D. Ryu, Astrophys. J. 764, 95 (2013). https://doi.org/10.1088/0004-637X/764/1/95

  366. S.E. Hong, D. Ryu, H. Kang, R. Cen, Astrophys. J. 785, 133 (2014). https://doi.org/10.1088/0004-637X/785/2/133

  367. S. Gabici, P. Blasi, Astrophys. J. 583, 695 (2003). https://doi.org/10.1086/345429

  368. V.S. Berezinsky, P. Blasi, V.S. Ptuskin, Astrophys. J. 487, 529 (1997). https://doi.org/10.1086/304622

  369. M. Lemoine, G. Pelletier, B. Revenu, Astrophys. J. 645, L129 (2006). https://doi.org/10.1086/506322

  370. P. Schneider, J.G. Kirk, Astrophys. J. Lett. 323, L87 (1987). https://doi.org/10.1086/185063

  371. D.C. Ellison, S.P. Reynolds, F.C. Jones, Astrophys. J. 360, 702 (1990). https://doi.org/10.1086/169156

  372. J.G. Kirk, A.W. Guthmann, Y.A. Gallant, A. Achterberg, Astrophys. J. 542, 235 (2000). https://doi.org/10.1086/309533

  373. M. Vietri, Astrophys. J. 591, 954 (2003). https://doi.org/10.1086/375534

  374. M. Vietri, D. De Marco, D. Guetta, Astrophys. J. 592, 378 (2003). https://doi.org/10.1086/375719

  375. P. Blasi, M. Vietri, Astrophys. J. 626, 877 (2005). https://doi.org/10.1086/430164

  376. Z. Li, E. Waxman, Astrophys. J. 651, 328 (2006). https://doi.org/10.1086/507413

  377. Z. Li, JCAP 1105, 008 (2011). https://doi.org/10.1088/1475-7516/2011/05/008

  378. L. Sironi, U. Keshet, M. Lemoine, Space Sci. Rev. 191(1–4), 519 (2015). https://doi.org/10.1007/s11214-015-0181-8

  379. L. Sironi, A. Spitkovsky, J. Arons, Astrophys. J. 771, 54 (2013). https://doi.org/10.1088/0004-637X/771/1/54

  380. A. Marcowith et al., Rept. Prog. Phys. 79, 046901 (2016). https://doi.org/10.1088/0034-4885/79/4/046901

  381. D. Caprioli, Astrophys. J. 811(2), L38 (2015). https://doi.org/10.1088/2041-8205/811/2/L38

  382. A. Venkatesan, M.C. Miller, A.V. Olinto, Astrophys. J. 484, 323 (1997). https://doi.org/10.1086/304304

  383. P. Blasi, R.I. Epstein, A.V. Olinto, Astrophys. J. 533, L123 (2000). https://doi.org/10.1086/312626

  384. J. Arons, Astrophys. J. 589, 871 (2003). https://doi.org/10.1086/374776

  385. K. Fang, K. Kotera, A.V. Olinto, JCAP 1303, 010 (2013). https://doi.org/10.1088/1475-7516/2013/03/010

  386. K. Kotera, E. Amato, P. Blasi, JCAP 1508(08), 026 (2015). https://doi.org/10.1088/1475-7516/2015/08/026

  387. D.R. Lorimer, Living Rev. Rel. 11, 8 (2008). https://doi.org/10.12942/lrr-2008-8

  388. M. Lemoine, Astron. Astrophys. 390, L31 (2002). https://doi.org/10.1051/0004-6361:20020939

  389. J. Pruet, S. Guiles, G.M. Fuller, Astrophys. J. 580, 368 (2002). https://doi.org/10.1086/342838

  390. S. Horiuchi, K. Murase, K. Ioka, P. Meszaros, Astrophys. J. 753, 69 (2012). https://doi.org/10.1088/0004-637X/753/1/69

  391. M. Ruderman, Ann. Rev. Astron. Astrophys. 10, 427 (1972). https://doi.org/10.1146/annurev.aa.10.090172.002235

  392. H.H. Chen, M.A. Ruderman, P.G. Sutherland, Astrophys. J. 191, 473 (1974). https://doi.org/10.1146/annurev.aa.10.090172.002235

  393. M.A. Ruderman, P.G. Sutherland, Astrophys. J. 196, 51 (1975). https://doi.org/10.1086/153393

  394. K.S. Cheng, C. Ho, M.A. Ruderman, Astrophys. J. 300, 500 (1986). https://doi.org/10.1086/163829

  395. R.J. Protheroe, W. Bednarek, Q. Luo, Astropart. Phys. 9, 1 (1998). https://doi.org/10.1016/S0927-6505(98)00014-0

  396. M. Takeda et al., Phys. Rev. Lett. 81, 1163 (1998). https://doi.org/10.1103/PhysRevLett.81.1163

  397. E. Schrodinger, Physica 6, 399 (1939)

    Article  Google Scholar 

  398. N.A. Chernikov, E.A. Tagirov, Ann. Inst. H. Poincare Phys. Theor. A9, 109 (1968)

    Google Scholar 

  399. L. Parker, Phys. Rev. Lett. 21, 562 (1968). https://doi.org/10.1103/PhysRevLett.21.562

  400. A. Grib, S. Mamayev, Sov. J. Nucl. Phys. 10, 722 (1970)

    Google Scholar 

  401. Ya.B. Zeldovich, A.A. Starobinsky, Sov. Phys. JETP 34, 1159 (1972). [Zh. Eksp. Teor. Fiz. 61, 2161 (1971)]

    Google Scholar 

  402. L.P. Grishchuk, Sov. Phys. JETP 40, 409 (1975). [Zh. Eksp. Teor. Fiz. 67, 825 (1974)]

    Google Scholar 

  403. D.J.H. Chung, E.W. Kolb, A. Riotto, Phys. Rev. D 59, 023501 (1999). https://doi.org/10.1103/PhysRevD.59.023501

  404. V. Kuzmin, I. Tkachev, JETP Lett. 68, 271 (1998). https://doi.org/10.1134/1.567858. [Pisma Zh. Eksp. Teor. Fiz. 68, 255 (1998)]

  405. D.J.H. Chung, E.W. Kolb, A. Riotto, I.I. Tkachev, Phys. Rev. D 62, 043508 (2000). https://doi.org/10.1103/PhysRevD.62.043508

  406. D.J.H. Chung, P. Crotty, E.W. Kolb, A. Riotto, Phys. Rev. D 64, 043503 (2001). https://doi.org/10.1103/PhysRevD.64.043503

  407. E.W. Kolb, A.A. Starobinsky, I.I. Tkachev, JCAP 0707, 005 (2007). https://doi.org/10.1088/1475-7516/2007/07/005

  408. M.A. Fedderke, E.W. Kolb, M. Wyman, Phys. Rev. D 91(6), 063505 (2015). https://doi.org/10.1103/PhysRevD.91.063505

  409. D. Ivanov, in PoS ICRC2015, vol. 349 (2016)

    Google Scholar 

  410. P. Blasi, R. Dick, E.W. Kolb, Astropart. Phys. 18, 57 (2002). https://doi.org/10.1016/S0927-6505(02)00113-5

  411. J. Abraham et al., Astropart. Phys. 29, 243 (2008). https://doi.org/10.1016/j.astropartphys.2008.01.003

  412. D.B. Cline, F.W. Stecker, in OWL/AW Neutrino Workshop on Observing Ultrahigh Energy Neutrinos, Los Angeles, California, November 1–3, 1999

    Google Scholar 

  413. A. Petrolini, Nucl. Instrum. Meth. A630, 131 (2011). https://doi.org/10.1016/j.nima.2010.06.044

  414. P. Allison, J. Auffenberg, R. Bard, J. Beatty, D. Besson et al., Astropart. Phys. 35, 457 (2012). https://doi.org/10.1016/j.astropartphys.2011.11.010

  415. P. Allison et al., Astropart. Phys. 70, 62 (2015). https://doi.org/10.1016/j.astropartphys.2015.04.006

  416. D.A. Kirzhnits, V.A. Chechin, Yad. Fiz. 15, 1051 (1972)

    Google Scholar 

  417. R. Aloisio, P. Blasi, P.L. Ghia, A.F. Grillo, Phys. Rev. D 62, 053010 (2000). https://doi.org/10.1103/PhysRevD.62.053010

  418. R. Aloisio, P. Blasi, A. Galante, P.L. Ghia, A.F. Grillo, Astropart. Phys. 19, 127 (2003). https://doi.org/10.1016/S0927-6505(02)00196-2

  419. R. Aloisio, P. Blasi, A. Galante, A.F. Grillo, Lect. Notes Phys. 669, 1 (2005). https://doi.org/10.1007/11377306_1

  420. R. Aloisio, A. Galante, A.F. Grillo, S. Liberati, E. Luzio, F. Mendez, Phys. Rev. D 74, 085017 (2006). https://doi.org/10.1103/PhysRevD.74.085017

  421. S. Liberati, Class. Quantum Grav. 30, 133001 (2013). https://doi.org/10.1088/0264-9381/30/13/133001

  422. V.A. Kostelecky, N. Russell, Rev. Mod. Phys. 83, 11 (2011). https://doi.org/10.1103/RevModPhys.83.11

  423. J.M. Carmona, J.L. Cortes, F. Mercati, Phys. Rev. D 86, 084032 (2012). https://doi.org/10.1103/PhysRevD.86.084032

  424. F.R. Klinkhamer, M. Risse, Phys. Rev. D 77, 117901 (2008). https://doi.org/10.1103/PhysRevD.77.117901

  425. T. Jacobson, S. Liberati, D. Mattingly, Ann. Phys. 321, 150 (2006). https://doi.org/10.1016/j.aop.2005.06.004

  426. A. Saveliev, L. Maccione, G. Sigl, JCAP 1103, 046 (2011). https://doi.org/10.1088/1475-7516/2011/03/046

  427. R. Aloisio, D. Boncioli, A. di Matteo, P.L. Ghia, A.F. Grillo, S. Petrera, F. Salamida, Frascati Phys. Ser. 58, 274 (2014)

    Google Scholar 

  428. E. Waxman, Phys. Rev. Lett. 75, 386 (1995). https://doi.org/10.1103/PhysRevLett.75.386

  429. M. Vietri, Ap. J. 453, 883 (1995). https://doi.org/10.1086/176448

  430. D. Eichler, N. Globus, R. Kumar, E. Gavish, Astrophys. J. 821(2), L24 (2016). https://doi.org/10.3847/2041-8205/821/2/L24

  431. R. Kumar, D. Eichler, Astrophys. J. 781(1), 47 (2014). https://doi.org/10.1088/0004-637X/781/1/47

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Acknowledgements

This review paper sprang out of the workshop ‘Multiple Messengers and Challenges in Astroparticle Physics’, held at GSSI from 6 to 17 October 2014. The authors acknowledge all participants for making many discussions possible during and after the workshop. The authors are also grateful to their colleagues at the GSSI, at the Arcetri Astrophysical Observatory, at the LNGS, at the University of Salento and the University of L’Aquila for stimulating discussions on the topics illustrated in the review.

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Aloisio, R., Blasi, P., De Mitri, I., Petrera, S. (2018). Selected Topics in Cosmic Ray Physics. In: Aloisio, R., Coccia, E., Vissani, F. (eds) Multiple Messengers and Challenges in Astroparticle Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-65425-6_1

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